LEC-9 CL 601 Mohr-Coloumb Soil Modelling.pptx

Constitutive modeling of soil;
Constitutive modelling;
Mohr- Coloumb Soil Modelling;
Computational Géotechnique;
Mohr-coloumb constitutive modelling;
soil friction angle;
drained test;
undrained test;;
Critical State soil mechanics
M Tech geotechnical Engg.;

1. Constitutive Modelling of Geomaterials Prof. Samirsinh P Parmar Mail: [email protected] Asst. Prof. Department of Civil Engineering, Faculty of Technology, Dharmasinh Desai University, Nadiad , Gujarat, INDIA Lecture: : Mohr- Coloumb Soil Modelling (Computational Géotechnique)

2. Idealized and Real Stress-Strain Behavior of Soils Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 2

3. Basic Concepts of Mohr-Coulomb Model B ili nea r app r o x i m a t i o n o f t r i a x i a l te s t Ba s i c l a w: for f    r evers i b l e e l ast i c s t r a i n  irr e v e rs i b l e p l a s ti c s tr a in f  f (  x ,  y ,  z ,  xy ,  yz ,  zx ) f = y i e l d f unc ti on    i i i e   p i  x , y , e t c. i e  p i   i  p Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 3

4. M ohr-Cou l o mb S o il M ode li ng Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 4

5. M ohr-Cou l o mb S o il M ode li ng F l o w ru le for p lastic strain: T his m eans: , , e tc.  i  p     g i  x  p      g x     y p   g y Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 5

6. M ohr-Cou l o mb S o il M ode li ng   a multiplier that determines the magnit ude of plastic strains  g   de t e r m i ne s t h e d i r e c ti o n o f p l a s ti c strain Cl a ss i c a l a ss o c i a te d p l a s t i c i t y : g = f G ene r a l non - a ss o c i a te d p l a s t i c i t y : g  f M-C m ode l: f  r – s s i n  – c c o s  : y i e l d fun c t i on g  r – s s i n  – c c o s  : p l a s t i c po t en t i a l fun c t i on i Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 6

7. M ohr-Cou l o mb S o il M ode li ng N on li nea r F a il ur e E nve l ope R e pr e s en t a ti on Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 7

8. M ohr-Cou l o mb S o il M ode li ng F ric ti o n A ng l e Defin iti o ns Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 8

9. M ohr-Cou l o mb S o il M ode li ng St r eng t h E nve l ope s for a R ange of S o i l T ype s Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 9

10. M ohr-Cou l o mb S o il M ode li ng  t c Ver sus R e l a ti v e D ens it y an d U n i t We i gh t Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 10

11. Fr icti o n A ng le D il a t anc y A ng l e R e l a ti ons h i ps Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 11

12. i n wh i c h:   1 = C o r r ec t i o n f o r p ar t i c l e s h a p e   1 = -6 o For high sphericity and subrounded shape For low sphericity and angular shape   1 = + 2 o   2 = C o r r ec t i o n f o r p ar t i c l e s i ze (effe c t i v e s i ze, d 1 )   2 = - 1 1   2 = - 9 o   2 = -4   2 = o For d 10 > 2.0 mm (gravel) For 2.0 > d 10 >0.6 mm (coarse sand) For 0.6 > d 10 >0.2 mm (medium sand) For 0.2 > d 10 >0.06 mm (fine sand) o   3 = C o r r ec t i o n f o r g ra d u a t i o n ( u n i f o r m i t y c o eff i c i e n t , C u )   3 = -2 o For C u > 2.0 (well-graded) For C u = 2.0 (medium graded) For C u < 2.0 (poorly graded)   3 = - 1 o   3 =   4 = C o r r ec t i o n f o r re l a t i v e d e n s i t y ( D r )   4 = -1   4 = o For 0 < D r <0.5 (loose) For 0.5 < D r < 0.75 (intermediate) For 0.75 < D r < 1.00 (dense)   4 = + 4 o  tc  36       o 1 2    3       4 5  5 = Correction for type of mineral  5 = 0  5 = +4 o  5 = +6 o For quartz For feldspar, calcite, chlorite For muscovite mica Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 12

13.  cv  m ax   cv  0. 8  for N C C l a ys vs. P I Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 13

14. Influence of Intermediate Principal Stress on Friction Angle Introduction: Models and soil mechanics S p ec i al c o n d iti o n s N a m e o f t e s t D i a g r a m  a   b   c T r u e t r i a x i al  b   c   r Cylindrical compression The “triaxial” test  b  P l a n e st ra i n o r b i a x ial  b  P l a n e st re s s  b   c   r  One-dimensional compression The oedometer test  b   c   r  Uniaxial compression or Unconfined compression  a   b   c  I s o t r op i c c o m p re ssi on Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 14

15. Influence of Intermediate Principal Stress on Friction Angle Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 15

16. Dra i ne d Sim p le Shear Te st Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 16

17. Ho w to Under stand   =  +  i or  =  -  i  i = inter particle angle of friction quartz sand:    – 30 o Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 17

18. Dra i ne d Tr i a xi a l Te st  v   x   y   z  2  x   y t a n   2 s i n  1  s i n  (iden ti c al t o b i a x i al t e s t) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 18

19. STRESS-STRAIN BEHAVIOR, VOLUME CHANGE, AND SHEARING OF SANDS Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 19

20. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 20

21. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 21

22. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 22

23. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 23

24. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 24

25. CR I T I CA L STATE Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 25

26. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 26

27. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 27

28. C r i t i c al S tate Definition: It is the soil state at which shearing occurs at constant volume and constant shearing stress At critical state, soil density and stress are in equilibrium, that is, the soil has no need to contract or dilate Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 28

29. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 29

30. SOURCES OF DRAINED SHEAR STRENGTH Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 30

31. What factors contribute to the strength of sand? D e nsity C o nfin e m e nt Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 31

32. S a n d – E ffe c t of D R q  d D r ai ne d  n o e x c es s p o r e press u r e C D t r ia x ial t es ts on dens e a n d loo s e s a n d spe cim ens Same i n itial co n fi n i n g s t res s b ut d iff eren t i n itial D R q   1   3 L oose s pecime n De nse s pecimen Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 32

33. q  d q   1   3 L oose s pecime n De nse s pecimen  v ol L oose s pecime n De nse s pecimen  d ( c o ntr a ct i o n ) ( di l a t i o n ) Dr a i ned  n o e x ce s s p o r e pre ss ure D il a t i ve Co n t ra c t i ve C R ITICA L S TATE Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 33

34. e Co n t ra c t i ve s p e c i m en e a t c ri t ica l st a te D il a t i ve s p e c i m en  d C r i t i c a l - s tat e v oid r atio e cs Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 34

35. S ources of s hear s t r ength F r i c ti o n be tw ee n s o il pa r ti cle s Pa r ti cl e re a rr ang e m e nt Int erl o ck ing be tw ee n pa r ti cles Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 35

36. S ources of s hear in g s trength Shearing strength of contractive sands is due primarily to friction between soil particles and particle rearrangement Shearing strength of dilative sands is due to interlocking between particles that has to be overcome by dilation (for dilation to occur, energy must be supplied to the soil for it to overcome the confining stress) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 36

37. S a n d – E ffe c t of c onfi nement  d D r ai ne d - n o e x c es s p o r e press u r e C D t r ia x ial t es ts on co n t r acti v e s a n d spe cim ens Same i n itial D R b ut d iff eren t i n itial co n fi n i n g s t res s q =  ’ 1 -  ’ 3  ’ 3   ’ 3   ’ 3 q cs 2q cs 3q cs Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 37

38.      c C r i t i c a l - s tat e en v elo p e  ’ 3   ’ 3   ’ 3   c  c Critical-state envelope  c A Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 38

39. D r ai ne d  n o e x c es s p o r e press u r e C D t r ia x ial t es ts on d ila t i v e s a n d spe cim ens Same i n itial D R b ut d iff eren t i n itial co n fi n i n g s t res s q =  ’ 1 -  ’ 3  d  ’ 3 q cs 1 / 2q cs 1 / 4q cs 1 / 2  ’ 3 1 / 4  ’ 3 S a n d – E ffe c t of c onfi nement Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 39

40.    C r i t i c a l - s tat e en v elo p e  ’ 3   ’ 3   ’ 3  c C ri t ica l - s t a te e n ve l o p e A     ’ 3     ’ 3 dil a t i ve c o n t ra c t i ve  c s   c   c   c   c Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 40

41. D r ai ne d  n o e x c es s p o r e press u r e C D t r ia x ial t es ts on d ila t i v e s a n d spe cim ens Same i n itial D R b ut d iff eren t i n itial co n fi n i n g s t res s q =  ’ 1 -  ’ 3 q peak 1/2  ’ 3 q peak 1/4  ’ 3  d  ’ 3 q cs S a n d – E ffe c t of c onfi nement Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 41

42.    P e ak an d cr iti c al - state e nv el o p e s  ’ 3   ’ 3   ’ 3  c C ri t ica l - s t a te e n ve l o p e A     ’ 3     ’ 3 Pe a k e n ve l o p e dil a t i ve c o n t ra c t i ve  c  pe ak  pe ak   c   c Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 42

43.    P e ak an d cr iti c al - state f r i c ti o n ang l e s  c C ri t ica l - s t a te e n ve l o p e Pe a k e n ve l o p e dil a t i ve c o n t ra c t i ve  pe ak  pe ak Hi gh e r  p e a k Low e r  p e a k u n t i l  c i s re a che d C o n fi n e m e n t Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 43

44. C r i t i c a l - s tat e f r i c t ion angle – Also called constant-volume  The  at very large strains  c = 28 o to 36 o  silica sands  c = 37 o to 44 o  carbonate sands Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 44

45. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 45

46. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 46

47. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 47

48. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 48

49. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 49

50. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 50

51. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 51

52. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 52

53. UNDRAINED SHEAR STRENGTH Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 53

54. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 54

55. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 55

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